Geodesic
Distribution properties of rows and columns for matrix linear recurrent sequences of the first order
Matematičeskie voprosy kriptografii, Tome 6 (2015), pp. 65-76.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider sequences of matrices over Galois ring satisfying linear recurrent equation of the first order. Estimates of the frequences of rows and columns in such sequences are obtained. These results generalize previously known bounds. 
@article{MVK_2015_6_a3,
     author = {O. V. Kamlovskiy},
     title = {Distribution properties of rows and columns for matrix linear recurrent sequences of the first order},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {65--76},
     publisher = {mathdoc},
     volume = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2015_6_a3/}
}
TY  - JOUR
AU  - O. V. Kamlovskiy
TI  - Distribution properties of rows and columns for matrix linear recurrent sequences of the first order
JO  - Matematičeskie voprosy kriptografii
PY  - 2015
SP  - 65
EP  - 76
VL  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MVK_2015_6_a3/
LA  - ru
ID  - MVK_2015_6_a3
ER  - 
%0 Journal Article
%A O. V. Kamlovskiy
%T Distribution properties of rows and columns for matrix linear recurrent sequences of the first order
%J Matematičeskie voprosy kriptografii
%D 2015
%P 65-76
%V 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MVK_2015_6_a3/
%G ru
%F MVK_2015_6_a3
O. V. Kamlovskiy. Distribution properties of rows and columns for matrix linear recurrent sequences of the first order. Matematičeskie voprosy kriptografii, Tome 6 (2015), pp. 65-76. http://geodesic.mathdoc.fr/item/MVK_2015_6_a3/

[1] Nechaev A. A., “Kod Kerdoka v tsiklicheskoi forme”, Diskret. matem., 1:4 (1989), 123–139 | MR | Zbl

[2] Nechaev V. I., “Raspredelenie znakov v posledovatelnosti pryamougolnykh matrits nad konechnym polem”, Trudy Matematicheskogo instituta imeni V. A. Steklova, 218, 1997, 335–342 | MR | Zbl

[3] Tsypyshev V. N., “Matrichnyi lineinyi kongruentnyi generator nad koltsom Galua nechetnoi kharakteristiki”, Chebyshevskii sbornik, 4:1 (2003), 112–124 | MR | Zbl

[4] Gentle J. E., Random number generation and Monte Carlo methods, Springer-Verlag, New York, 2003 | MR | Zbl

[5] Afflerbach L., Grothe H., “The lattice structure of pseudo-random vectors generated by matrix generators”, J. Comput. Appl. Math., 23 (1988), 127–131 | DOI | MR | Zbl

[6] Niederreiter H., “Statistical independence properties of pseudorandom vectors produced by matrix generators”, J. Comput. Appl. Math., 31 (1990), 139–151 | DOI | MR | Zbl

[7] Nechaev A. A., “Tsiklovye tipy lineinykh podstanovok nad konechnymi kommutativnymi koltsami”, Matem. sb., 184:3 (1993), 21–56 | MR | Zbl

[8] Kamlovskii O. V., “Chastotnye kharakteristiki lineinykh rekurrentnykh posledovatelnostei nad koltsami Galua”, Matem. sb., 200:4 (2009), 31–52 | DOI | MR | Zbl

[9] Kamlovskii O. V., “Chastotnye kharakteristiki razryadnykh posledovatelnostei lineinykh rekurrent nad koltsami Galua”, Izv. RAN. Ser. matem., 77:6 (2013), 71–96 | DOI | MR | Zbl

[10] Korobov N. M., “Raspredelenie nevychetov i pervoobraznykh kornei v rekurrentnykh ryadakh”, Doklady AN SSSR, 88:4 (1953), 603–606 | MR | Zbl

[11] Niederreiter H., “Distribution properties of feedback shift register sequences”, Probl. Control and Inform. Theory, 15:1 (1986), 19–34 | MR | Zbl

[12] Nechaev A. A., “O podobii matrits nad kommutativnym lokalnym artinovym koltsom”, Trudy seminara im. Petrovskogo I. G., 184, no. 9, 1983, 81–101 | MR

[13] Leng S., Algebra, Mir, M., 1968, 564 pp.

[14] Glukhov M. M., Elizarov V. P., Nechaev A. A., Algebra, Uchebnik, v. 2, Gelios ARV, M., 2003, 416 pp.